Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_pH 4 5.353372
beta0_pH 3 3.060905
beta1_black 7 1.750072
beta3_black 3 1.544981
beta2_pH 10 1.538679
beta0_black 4 1.459654
mu_beta0_pH 1 1.395640
beta0_pelagic 1 1.392569
beta1_pelagic 2 1.278769
beta1_yellow 1 1.276641
parameter n badRhat_avg
beta2_black 3 1.239688
beta1_pH 13 1.221033
beta_H 1 1.215523
beta3_yellow 1 1.209760
beta2_pelagic 4 1.204255
beta2_yellow 3 1.193039
tau_beta0_pH 1 1.184636
sd_comp 1 1.141493
beta0_yellow 1 1.119123
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_black 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0
beta0_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
beta0_pH 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0
beta0_yellow 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta1_black 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0
beta1_pelagic 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
beta1_pH 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0
beta1_yellow 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
beta2_black 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0
beta2_pelagic 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0
beta2_pH 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1
beta2_yellow 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0
beta3_black 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
beta3_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0
beta3_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
mu_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.133 0.071 -0.263 -0.135 0.012
mu_bc_H[2] -0.097 0.046 -0.177 -0.101 0.001
mu_bc_H[3] -0.434 0.072 -0.567 -0.438 -0.283
mu_bc_H[4] -0.990 0.193 -1.389 -0.983 -0.628
mu_bc_H[5] 0.894 1.034 -0.151 0.701 2.960
mu_bc_H[6] -2.203 0.317 -2.818 -2.212 -1.572
mu_bc_H[7] -0.474 0.111 -0.700 -0.469 -0.267
mu_bc_H[8] 0.245 0.351 -0.350 0.214 1.016
mu_bc_H[9] -0.301 0.135 -0.569 -0.305 -0.035
mu_bc_H[10] -0.112 0.067 -0.235 -0.115 0.024
mu_bc_H[11] -0.103 0.041 -0.181 -0.105 -0.019
mu_bc_H[12] -0.248 0.107 -0.473 -0.242 -0.039
mu_bc_H[13] -0.128 0.080 -0.278 -0.130 0.034
mu_bc_H[14] -0.277 0.098 -0.470 -0.276 -0.092
mu_bc_H[15] -0.348 0.053 -0.450 -0.348 -0.244
mu_bc_H[16] -0.283 0.384 -0.945 -0.306 0.513
mu_bc_R[1] 1.351 0.142 1.075 1.351 1.638
mu_bc_R[2] 1.490 0.088 1.316 1.490 1.663
mu_bc_R[3] 1.430 0.132 1.179 1.431 1.694
mu_bc_R[4] 0.983 0.192 0.585 0.989 1.329
mu_bc_R[5] 1.152 0.463 0.251 1.152 2.015
mu_bc_R[6] -1.547 0.427 -2.382 -1.546 -0.742
mu_bc_R[7] 0.305 0.192 -0.071 0.304 0.681
mu_bc_R[8] 0.530 0.200 0.114 0.535 0.901
mu_bc_R[9] 0.382 0.196 -0.031 0.398 0.725
mu_bc_R[10] 1.325 0.125 1.065 1.328 1.558
mu_bc_R[11] 1.143 0.079 0.989 1.145 1.299
mu_bc_R[12] 0.944 0.195 0.564 0.945 1.324
mu_bc_R[13] 1.086 0.100 0.890 1.085 1.281
mu_bc_R[14] 0.980 0.144 0.698 0.981 1.257
mu_bc_R[15] 0.911 0.099 0.719 0.908 1.111
mu_bc_R[16] 1.187 0.123 0.952 1.183 1.434
tau_pH[1] 2.811 0.272 2.297 2.802 3.359
tau_pH[2] 2.677 0.335 2.082 2.651 3.393
tau_pH[3] 2.913 0.411 2.166 2.914 3.730
beta0_pH[1,1] 0.542 0.226 0.102 0.548 0.967
beta0_pH[2,1] 1.280 0.232 0.791 1.284 1.714
beta0_pH[3,1] 1.372 0.254 0.826 1.386 1.866
beta0_pH[4,1] 1.636 0.274 1.053 1.652 2.137
beta0_pH[5,1] -0.506 0.443 -1.264 -0.528 0.658
beta0_pH[6,1] 0.136 0.611 -1.105 0.165 1.084
beta0_pH[7,1] 0.401 0.539 -0.783 0.629 1.026
beta0_pH[8,1] -0.570 0.321 -1.300 -0.534 -0.023
beta0_pH[9,1] -0.500 0.334 -1.245 -0.473 0.089
beta0_pH[10,1] 0.314 0.253 -0.187 0.315 0.808
beta0_pH[11,1] -0.268 0.248 -0.793 -0.258 0.187
beta0_pH[12,1] 0.446 0.284 -0.155 0.464 0.939
beta0_pH[13,1] -0.196 0.241 -0.700 -0.184 0.247
beta0_pH[14,1] -0.434 0.275 -1.041 -0.409 0.042
beta0_pH[15,1] -0.531 0.319 -1.264 -0.497 -0.017
beta0_pH[16,1] 0.297 1.320 -1.458 -0.302 2.497
beta0_pH[1,2] 2.656 0.224 2.151 2.684 3.029
beta0_pH[2,2] 2.895 0.214 2.374 2.916 3.237
beta0_pH[3,2] 2.408 0.293 1.799 2.427 2.937
beta0_pH[4,2] 2.604 0.293 1.868 2.675 2.999
beta0_pH[5,2] 4.403 1.578 1.970 4.175 8.228
beta0_pH[6,2] 2.842 0.309 2.275 2.863 3.358
beta0_pH[7,2] 1.890 0.199 1.451 1.908 2.222
beta0_pH[8,2] 2.763 0.331 2.068 2.804 3.130
beta0_pH[9,2] 2.838 0.622 1.589 2.972 3.711
beta0_pH[10,2] 3.661 0.248 3.050 3.690 4.065
beta0_pH[11,2] -4.848 0.275 -5.397 -4.845 -4.313
beta0_pH[12,2] -4.819 0.437 -5.763 -4.786 -4.056
beta0_pH[13,2] -4.629 0.394 -5.440 -4.626 -3.889
beta0_pH[14,2] -5.610 0.455 -6.539 -5.583 -4.788
beta0_pH[15,2] -4.147 0.307 -4.758 -4.140 -3.560
beta0_pH[16,2] -4.865 0.370 -5.634 -4.856 -4.190
beta0_pH[1,3] 1.279 0.335 0.489 1.317 1.764
beta0_pH[2,3] 1.973 0.377 1.104 2.066 2.451
beta0_pH[3,3] 2.158 0.399 1.253 2.253 2.717
beta0_pH[4,3] 2.522 0.564 1.144 2.746 3.150
beta0_pH[5,3] 1.178 2.260 -3.940 1.142 5.789
beta0_pH[6,3] -1.002 1.500 -2.581 -1.486 3.253
beta0_pH[7,3] -1.896 0.961 -3.642 -1.956 0.583
beta0_pH[8,3] 0.306 0.175 -0.040 0.308 0.655
beta0_pH[9,3] -0.035 0.340 -0.690 -0.030 0.608
beta0_pH[10,3] 0.803 0.281 0.190 0.818 1.298
beta0_pH[11,3] -0.117 0.330 -0.895 -0.103 0.514
beta0_pH[12,3] -0.994 0.331 -1.676 -0.983 -0.368
beta0_pH[13,3] -0.016 0.296 -0.661 -0.002 0.518
beta0_pH[14,3] -0.158 0.249 -0.648 -0.161 0.344
beta0_pH[15,3] -0.674 0.307 -1.292 -0.666 -0.104
beta0_pH[16,3] -0.521 0.360 -1.191 -0.486 0.126
beta1_pH[1,1] 3.095 0.399 2.417 3.071 3.988
beta1_pH[2,1] 2.454 0.385 1.790 2.419 3.307
beta1_pH[3,1] 2.598 0.533 1.772 2.524 3.901
beta1_pH[4,1] 3.080 0.663 2.194 2.955 4.831
beta1_pH[5,1] 2.042 0.509 1.097 2.017 3.077
beta1_pH[6,1] 2.629 1.000 1.240 2.416 5.232
beta1_pH[7,1] 2.125 1.318 0.284 1.995 4.865
beta1_pH[8,1] 3.411 1.057 2.095 3.162 6.164
beta1_pH[9,1] 2.159 0.463 1.436 2.098 3.279
beta1_pH[10,1] 2.281 0.361 1.610 2.270 3.007
beta1_pH[11,1] 6.696 0.927 5.221 6.560 8.882
beta1_pH[12,1] 2.937 0.336 2.324 2.924 3.662
beta1_pH[13,1] 6.220 1.500 4.220 5.847 10.029
beta1_pH[14,1] 14.516 4.223 8.892 13.528 25.330
beta1_pH[15,1] 8.004 1.737 5.585 7.655 12.467
beta1_pH[16,1] 11.924 2.835 6.971 11.896 17.070
beta1_pH[1,2] 10.250 41.743 0.003 1.072 122.092
beta1_pH[2,2] 6.690 13.574 0.013 1.555 45.079
beta1_pH[3,2] 1.279 0.561 0.658 1.245 1.975
beta1_pH[4,2] 7.506 47.427 0.006 1.032 38.255
beta1_pH[5,2] 110.723 453.992 0.000 0.586 1916.591
beta1_pH[6,2] 1.295 3.017 0.000 0.983 4.971
beta1_pH[7,2] 0.941 2.124 0.000 0.189 7.944
beta1_pH[8,2] 1.507 6.305 0.000 0.152 11.559
beta1_pH[9,2] 1.270 3.948 0.000 0.860 3.325
beta1_pH[10,2] 5.761 15.208 0.000 1.239 53.837
beta1_pH[11,2] 6.714 0.304 6.114 6.708 7.307
beta1_pH[12,2] 6.668 0.564 5.743 6.604 7.943
beta1_pH[13,2] 7.094 0.431 6.286 7.092 7.970
beta1_pH[14,2] 7.494 0.480 6.625 7.469 8.496
beta1_pH[15,2] 6.669 0.332 6.020 6.662 7.342
beta1_pH[16,2] 7.579 0.396 6.842 7.571 8.402
beta1_pH[1,3] 2.038 0.601 1.207 1.976 3.415
beta1_pH[2,3] 0.997 2.231 0.001 0.470 6.217
beta1_pH[3,3] 1.325 6.615 0.001 0.527 7.951
beta1_pH[4,3] 2.499 7.497 0.001 0.557 31.749
beta1_pH[5,3] 4.686 5.564 1.394 3.055 20.358
beta1_pH[6,3] 3.848 4.287 1.320 2.933 12.371
beta1_pH[7,3] 2.740 0.945 0.346 2.782 4.488
beta1_pH[8,3] 2.701 0.315 2.091 2.695 3.314
beta1_pH[9,3] 2.139 0.397 1.377 2.146 2.878
beta1_pH[10,3] 2.588 0.352 1.969 2.575 3.328
beta1_pH[11,3] 2.813 0.394 2.115 2.793 3.746
beta1_pH[12,3] 4.340 0.409 3.570 4.338 5.164
beta1_pH[13,3] 2.165 0.333 1.534 2.143 2.914
beta1_pH[14,3] 2.641 0.309 2.040 2.636 3.253
beta1_pH[15,3] 2.521 0.350 1.887 2.508 3.254
beta1_pH[16,3] 2.133 0.301 1.520 2.136 2.713
beta2_pH[1,1] 0.496 0.181 0.262 0.466 0.916
beta2_pH[2,1] 0.503 0.323 0.199 0.438 1.158
beta2_pH[3,1] 0.458 0.350 0.163 0.391 1.102
beta2_pH[4,1] 0.378 0.157 0.164 0.351 0.744
beta2_pH[5,1] 1.263 1.554 0.081 0.627 5.723
beta2_pH[6,1] 0.863 1.499 0.103 0.334 5.662
beta2_pH[7,1] -0.544 1.576 -4.700 -0.013 1.432
beta2_pH[8,1] 0.383 0.432 0.132 0.296 1.153
beta2_pH[9,1] 0.659 0.834 0.157 0.458 2.580
beta2_pH[10,1] 0.807 0.745 0.256 0.583 2.752
beta2_pH[11,1] 0.234 0.051 0.150 0.229 0.346
beta2_pH[12,1] 1.023 0.531 0.405 0.903 2.392
beta2_pH[13,1] 0.247 0.072 0.141 0.236 0.418
beta2_pH[14,1] 0.249 0.041 0.178 0.246 0.342
beta2_pH[15,1] 0.208 0.048 0.131 0.203 0.312
beta2_pH[16,1] 0.342 0.347 0.122 0.180 1.128
beta2_pH[1,2] -1.842 4.038 -9.617 -1.998 5.680
beta2_pH[2,2] -3.449 3.170 -10.492 -3.099 2.856
beta2_pH[3,2] -3.847 2.689 -10.534 -3.177 -0.619
beta2_pH[4,2] -3.874 3.134 -10.998 -3.415 1.490
beta2_pH[5,2] -2.005 4.090 -10.433 -2.045 6.061
beta2_pH[6,2] -2.908 3.762 -10.277 -2.813 5.803
beta2_pH[7,2] -2.843 3.875 -10.516 -2.846 5.634
beta2_pH[8,2] -2.455 3.957 -10.269 -2.574 6.045
beta2_pH[9,2] -2.964 3.721 -10.047 -2.983 5.671
beta2_pH[10,2] -3.369 3.876 -11.231 -3.334 5.504
beta2_pH[11,2] -7.300 2.590 -13.706 -6.806 -3.692
beta2_pH[12,2] -3.561 2.851 -10.427 -2.679 -0.585
beta2_pH[13,2] -4.012 2.506 -10.386 -3.224 -1.369
beta2_pH[14,2] -5.011 2.517 -11.387 -4.462 -1.788
beta2_pH[15,2] -7.039 2.610 -13.316 -6.512 -3.459
beta2_pH[16,2] -7.239 2.636 -13.617 -6.707 -3.654
beta2_pH[1,3] 3.404 2.510 0.266 2.897 9.466
beta2_pH[2,3] 1.818 3.949 -6.331 1.817 9.816
beta2_pH[3,3] 1.283 4.252 -7.295 1.540 9.930
beta2_pH[4,3] 1.464 4.155 -6.326 1.590 9.844
beta2_pH[5,3] 5.630 3.010 0.553 5.440 12.115
beta2_pH[6,3] 5.840 2.936 0.958 5.542 12.738
beta2_pH[7,3] 6.055 2.642 1.352 5.869 12.518
beta2_pH[8,3] 6.837 2.741 2.522 6.418 13.444
beta2_pH[9,3] 5.803 2.707 1.629 5.439 11.905
beta2_pH[10,3] 5.449 2.869 0.776 5.148 12.027
beta2_pH[11,3] -1.439 0.933 -3.714 -1.264 -0.472
beta2_pH[12,3] -1.681 0.843 -3.731 -1.497 -0.877
beta2_pH[13,3] -2.039 1.440 -6.317 -1.627 -0.687
beta2_pH[14,3] -2.012 1.365 -5.936 -1.640 -0.795
beta2_pH[15,3] -2.044 1.439 -6.322 -1.623 -0.813
beta2_pH[16,3] -0.231 2.354 -3.076 -1.208 5.550
beta3_pH[1,1] 35.754 1.073 33.757 35.723 37.923
beta3_pH[2,1] 34.024 1.614 31.151 33.867 37.656
beta3_pH[3,1] 35.683 1.927 32.545 35.442 40.378
beta3_pH[4,1] 36.214 2.034 32.916 35.980 41.132
beta3_pH[5,1] 29.342 3.138 25.602 28.288 36.914
beta3_pH[6,1] 40.436 3.345 32.737 41.413 45.198
beta3_pH[7,1] 29.440 9.728 18.457 25.101 45.785
beta3_pH[8,1] 39.023 2.336 34.838 38.880 44.753
beta3_pH[9,1] 31.156 2.109 27.581 31.020 35.792
beta3_pH[10,1] 32.882 1.240 30.686 32.813 35.461
beta3_pH[11,1] 35.662 1.485 33.089 35.493 39.293
beta3_pH[12,1] 30.370 0.601 29.070 30.400 31.447
beta3_pH[13,1] 39.020 2.441 35.340 38.603 44.773
beta3_pH[14,1] 41.261 2.034 37.788 41.058 45.469
beta3_pH[15,1] 39.043 2.265 35.765 38.675 44.677
beta3_pH[16,1] 43.837 1.731 39.500 44.273 45.919
beta3_pH[1,2] 30.945 8.723 18.542 28.560 44.259
beta3_pH[2,2] 28.274 5.802 18.546 28.231 42.346
beta3_pH[3,2] 41.623 2.030 39.663 41.826 43.860
beta3_pH[4,2] 29.714 9.018 18.520 25.737 44.752
beta3_pH[5,2] 30.777 8.233 18.576 30.036 45.205
beta3_pH[6,2] 33.317 5.920 19.348 35.061 44.581
beta3_pH[7,2] 29.270 7.598 18.446 28.297 44.711
beta3_pH[8,2] 28.949 7.467 18.527 27.696 44.480
beta3_pH[9,2] 37.279 9.076 19.098 43.116 45.728
beta3_pH[10,2] 30.227 6.171 19.225 29.683 43.368
beta3_pH[11,2] 43.392 0.147 43.148 43.373 43.704
beta3_pH[12,2] 43.158 0.235 42.593 43.156 43.638
beta3_pH[13,2] 43.834 0.145 43.516 43.855 44.080
beta3_pH[14,2] 43.316 0.161 43.075 43.294 43.677
beta3_pH[15,2] 43.406 0.158 43.143 43.393 43.735
beta3_pH[16,2] 43.491 0.160 43.199 43.488 43.808
beta3_pH[1,3] 39.995 0.986 37.671 40.066 41.445
beta3_pH[2,3] 31.130 7.398 18.645 32.124 44.642
beta3_pH[3,3] 30.845 7.522 18.476 31.820 44.121
beta3_pH[4,3] 27.501 7.089 18.327 26.295 44.304
beta3_pH[5,3] 26.815 6.129 18.340 26.387 41.882
beta3_pH[6,3] 30.475 4.418 19.686 31.719 39.124
beta3_pH[7,3] 25.599 2.663 22.306 24.924 30.011
beta3_pH[8,3] 41.494 0.216 41.106 41.490 41.885
beta3_pH[9,3] 33.753 0.449 32.979 33.780 34.668
beta3_pH[10,3] 36.101 0.454 35.081 36.119 36.847
beta3_pH[11,3] 41.591 0.727 40.187 41.571 43.032
beta3_pH[12,3] 41.751 0.352 41.055 41.752 42.442
beta3_pH[13,3] 42.160 0.718 40.875 42.123 43.646
beta3_pH[14,3] 40.911 0.537 39.827 40.943 41.910
beta3_pH[15,3] 42.113 0.624 40.921 42.083 43.293
beta3_pH[16,3] 38.069 6.104 29.066 41.904 43.511
beta0_pelagic[1] 1.780 0.520 0.440 1.971 2.382
beta0_pelagic[2] 1.268 0.395 0.201 1.394 1.713
beta0_pelagic[3] 0.071 0.846 -2.888 0.313 0.813
beta0_pelagic[4] 0.233 0.494 -1.057 0.314 1.042
beta0_pelagic[5] 0.338 1.500 -2.968 1.210 1.652
beta0_pelagic[6] 1.546 0.221 1.024 1.576 1.848
beta0_pelagic[7] 1.528 0.141 1.244 1.532 1.786
beta0_pelagic[8] 1.850 0.153 1.530 1.855 2.132
beta0_pelagic[9] 1.901 0.830 -0.200 2.026 2.856
beta0_pelagic[10] 2.519 0.252 1.665 2.563 2.812
beta0_pelagic[11] 0.666 0.132 0.413 0.666 0.924
beta0_pelagic[12] 1.757 0.132 1.496 1.757 2.018
beta0_pelagic[13] 0.518 0.143 0.229 0.523 0.789
beta0_pelagic[14] 0.402 0.176 0.018 0.413 0.731
beta0_pelagic[15] -0.270 0.129 -0.520 -0.267 -0.014
beta0_pelagic[16] 0.566 0.128 0.308 0.567 0.813
beta1_pelagic[1] 0.474 0.535 0.000 0.278 1.842
beta1_pelagic[2] 0.322 0.395 0.000 0.147 1.332
beta1_pelagic[3] 1.237 1.642 0.130 0.760 7.387
beta1_pelagic[4] 0.954 0.517 0.006 0.879 2.302
beta1_pelagic[5] 1.123 1.618 0.000 0.010 4.667
beta1_pelagic[6] 0.127 0.436 0.000 0.002 0.997
beta1_pelagic[7] 0.601 1.929 0.000 0.002 6.895
beta1_pelagic[8] 0.151 0.585 0.000 0.002 1.197
beta1_pelagic[9] 0.970 0.983 0.000 0.893 3.485
beta1_pelagic[10] 0.129 0.445 0.000 0.002 1.186
beta1_pelagic[11] 2.415 0.238 1.932 2.421 2.881
beta1_pelagic[12] 2.628 0.259 2.135 2.628 3.128
beta1_pelagic[13] 2.367 0.448 1.592 2.321 3.351
beta1_pelagic[14] 2.991 0.590 2.126 2.885 4.521
beta1_pelagic[15] 2.553 0.223 2.113 2.550 2.992
beta1_pelagic[16] 2.965 0.253 2.496 2.959 3.485
beta2_pelagic[1] 2.135 2.873 -3.459 1.623 8.901
beta2_pelagic[2] 2.183 2.908 -3.320 1.659 9.118
beta2_pelagic[3] 1.956 2.368 0.023 1.162 8.592
beta2_pelagic[4] 2.536 2.512 0.176 1.715 9.008
beta2_pelagic[5] -0.436 3.733 -7.070 -1.129 7.670
beta2_pelagic[6] 0.640 3.943 -7.577 0.745 8.611
beta2_pelagic[7] 0.226 3.651 -7.654 0.366 7.176
beta2_pelagic[8] 0.357 3.538 -6.695 0.441 7.043
beta2_pelagic[9] 1.432 3.311 -6.255 1.154 8.163
beta2_pelagic[10] 0.576 3.780 -7.263 0.691 8.240
beta2_pelagic[11] 4.261 2.505 0.956 3.649 10.429
beta2_pelagic[12] 5.069 2.516 1.974 4.450 11.667
beta2_pelagic[13] 1.455 1.708 0.293 0.789 6.737
beta2_pelagic[14] 0.591 0.496 0.242 0.490 1.522
beta2_pelagic[15] 5.536 2.605 2.252 4.792 12.045
beta2_pelagic[16] 5.480 2.718 1.343 5.056 12.076
beta3_pelagic[1] 25.897 6.939 18.343 23.194 43.770
beta3_pelagic[2] 26.656 7.909 18.301 23.611 44.882
beta3_pelagic[3] 30.382 5.028 21.510 30.054 42.783
beta3_pelagic[4] 25.255 3.216 20.259 25.111 35.161
beta3_pelagic[5] 35.479 9.860 18.809 37.130 45.989
beta3_pelagic[6] 30.005 8.010 18.458 29.046 44.838
beta3_pelagic[7] 28.912 8.112 18.472 27.639 44.790
beta3_pelagic[8] 29.643 7.864 18.421 28.302 44.858
beta3_pelagic[9] 28.563 5.945 19.091 26.675 43.114
beta3_pelagic[10] 29.301 8.074 18.420 28.153 44.840
beta3_pelagic[11] 43.219 0.319 42.515 43.225 43.799
beta3_pelagic[12] 43.455 0.235 43.045 43.448 43.907
beta3_pelagic[13] 42.813 0.957 40.879 42.846 44.938
beta3_pelagic[14] 42.709 1.166 40.338 42.734 44.946
beta3_pelagic[15] 43.234 0.217 42.782 43.229 43.658
beta3_pelagic[16] 43.272 0.239 42.731 43.276 43.694
mu_beta0_pelagic[1] 0.777 0.848 -1.133 0.820 2.352
mu_beta0_pelagic[2] 1.565 0.671 -0.215 1.685 2.559
mu_beta0_pelagic[3] 0.593 0.421 -0.264 0.594 1.401
tau_beta0_pelagic[1] 1.814 4.791 0.062 0.730 9.507
tau_beta0_pelagic[2] 3.154 6.089 0.080 1.558 17.040
tau_beta0_pelagic[3] 1.880 1.438 0.220 1.519 5.576
beta0_yellow[1] -0.530 0.182 -0.958 -0.515 -0.215
beta0_yellow[2] 0.482 0.193 -0.020 0.503 0.773
beta0_yellow[3] -0.310 0.172 -0.669 -0.306 0.006
beta0_yellow[4] 0.780 0.380 -0.447 0.871 1.193
beta0_yellow[5] -1.222 0.417 -2.045 -1.216 -0.406
beta0_yellow[6] 0.243 0.213 -0.180 0.242 0.664
beta0_yellow[7] 0.866 0.580 -1.006 1.027 1.347
beta0_yellow[8] 0.770 0.566 -0.911 0.958 1.285
beta0_yellow[9] -0.051 0.278 -0.580 -0.051 0.477
beta0_yellow[10] 0.243 0.148 -0.041 0.243 0.535
beta0_yellow[11] -1.912 0.423 -2.738 -1.915 -1.075
beta0_yellow[12] -3.592 0.407 -4.412 -3.587 -2.820
beta0_yellow[13] -3.563 0.454 -4.489 -3.525 -2.772
beta0_yellow[14] -2.023 0.586 -2.989 -2.102 -0.343
beta0_yellow[15] -2.900 0.413 -3.740 -2.884 -2.099
beta0_yellow[16] -2.346 0.447 -3.249 -2.335 -1.439
beta1_yellow[1] 0.465 0.480 0.000 0.373 1.577
beta1_yellow[2] 1.112 0.474 0.610 1.026 2.629
beta1_yellow[3] 0.658 0.256 0.163 0.654 1.134
beta1_yellow[4] 1.568 1.044 0.667 1.213 4.787
beta1_yellow[5] 3.839 5.294 1.369 2.887 20.222
beta1_yellow[6] 2.302 0.343 1.646 2.304 2.973
beta1_yellow[7] 5.865 6.502 0.299 3.863 26.755
beta1_yellow[8] 2.973 4.596 0.034 1.932 14.550
beta1_yellow[9] 1.538 0.457 0.826 1.504 2.574
beta1_yellow[10] 2.616 0.482 1.759 2.581 3.688
beta1_yellow[11] 2.059 0.421 1.228 2.059 2.875
beta1_yellow[12] 2.377 0.419 1.577 2.366 3.233
beta1_yellow[13] 2.748 0.454 1.962 2.721 3.695
beta1_yellow[14] 2.104 0.534 0.897 2.132 3.079
beta1_yellow[15] 2.200 0.411 1.394 2.191 3.028
beta1_yellow[16] 2.143 0.444 1.280 2.135 3.063
beta2_yellow[1] -2.937 2.974 -9.492 -2.524 2.373
beta2_yellow[2] -3.215 2.639 -9.609 -2.569 -0.120
beta2_yellow[3] -3.438 2.580 -9.343 -3.038 -0.176
beta2_yellow[4] -2.707 2.686 -8.932 -1.944 -0.073
beta2_yellow[5] -4.382 2.913 -11.359 -3.902 -0.481
beta2_yellow[6] 3.607 2.207 0.939 3.067 9.358
beta2_yellow[7] -3.874 3.956 -11.351 -3.906 5.401
beta2_yellow[8] -2.793 4.038 -10.743 -2.514 5.915
beta2_yellow[9] 3.797 2.544 0.254 3.435 9.678
beta2_yellow[10] -4.923 2.860 -11.572 -4.311 -1.045
beta2_yellow[11] -3.523 1.911 -8.805 -2.996 -1.268
beta2_yellow[12] -3.826 2.072 -9.573 -3.271 -1.323
beta2_yellow[13] -3.747 1.869 -8.735 -3.272 -1.487
beta2_yellow[14] -3.734 2.196 -9.437 -3.190 -0.739
beta2_yellow[15] -3.252 1.778 -7.976 -2.856 -1.082
beta2_yellow[16] -3.874 2.024 -9.286 -3.325 -1.430
beta3_yellow[1] 27.912 7.401 18.451 25.903 44.669
beta3_yellow[2] 29.006 1.945 24.199 28.859 32.986
beta3_yellow[3] 32.963 2.752 26.862 32.911 38.488
beta3_yellow[4] 28.583 3.720 20.165 27.870 36.002
beta3_yellow[5] 33.144 2.002 27.390 33.391 35.547
beta3_yellow[6] 39.656 0.512 38.736 39.629 40.805
beta3_yellow[7] 21.156 3.494 18.516 20.166 31.418
beta3_yellow[8] 26.102 5.269 18.401 25.955 40.670
beta3_yellow[9] 37.866 2.002 36.222 37.606 43.239
beta3_yellow[10] 29.362 0.434 28.351 29.410 29.993
beta3_yellow[11] 45.399 0.468 44.264 45.493 45.978
beta3_yellow[12] 43.376 0.441 42.526 43.338 44.350
beta3_yellow[13] 44.813 0.400 43.940 44.874 45.482
beta3_yellow[14] 43.836 2.568 33.233 44.229 45.876
beta3_yellow[15] 45.358 0.476 44.332 45.436 45.978
beta3_yellow[16] 44.627 0.619 43.463 44.632 45.808
mu_beta0_yellow[1] 0.086 0.551 -1.080 0.098 1.222
mu_beta0_yellow[2] 0.107 0.478 -0.906 0.123 0.996
mu_beta0_yellow[3] -2.413 0.613 -3.417 -2.507 -0.884
tau_beta0_yellow[1] 2.080 3.571 0.095 1.219 8.216
tau_beta0_yellow[2] 1.391 1.645 0.149 1.051 4.535
tau_beta0_yellow[3] 1.582 2.141 0.116 1.014 6.421
beta0_black[1] 0.003 0.196 -0.352 -0.004 0.377
beta0_black[2] 1.866 0.166 1.501 1.879 2.125
beta0_black[3] 1.273 0.172 0.899 1.286 1.553
beta0_black[4] 2.142 0.308 1.538 2.148 2.615
beta0_black[5] 1.504 1.973 -3.347 1.583 5.435
beta0_black[6] 1.552 1.999 -3.056 1.614 5.498
beta0_black[7] 1.594 1.926 -2.791 1.634 5.565
beta0_black[8] 1.242 0.232 0.786 1.245 1.679
beta0_black[9] 2.402 0.284 1.833 2.414 2.907
beta0_black[10] 1.457 0.128 1.202 1.456 1.704
beta0_black[11] 3.229 0.770 0.825 3.408 3.726
beta0_black[12] 4.469 0.196 4.069 4.475 4.843
beta0_black[13] -0.115 0.236 -0.600 -0.105 0.304
beta0_black[14] 1.960 0.700 0.074 2.173 2.748
beta0_black[15] 1.098 0.411 -0.102 1.190 1.523
beta0_black[16] 3.983 0.701 1.697 4.199 4.541
beta2_black[1] 2.303 3.522 -6.187 2.364 9.160
beta2_black[2] -0.676 4.060 -9.550 -0.713 7.478
beta2_black[3] -0.066 4.271 -8.932 0.088 8.307
beta2_black[4] -2.028 3.754 -10.102 -1.713 6.598
beta2_black[5] -0.399 4.321 -8.907 -0.561 8.249
beta2_black[6] -0.336 4.190 -8.526 -0.400 8.476
beta2_black[7] -0.265 4.277 -8.423 -0.454 8.668
beta2_black[8] -0.555 4.230 -8.417 -0.706 8.209
beta2_black[9] -0.413 4.321 -8.979 -0.406 8.202
beta2_black[10] -0.444 4.237 -8.791 -0.578 8.540
beta2_black[11] -1.630 2.290 -7.174 -1.339 3.019
beta2_black[12] -2.472 1.889 -8.264 -1.925 -0.450
beta2_black[13] -2.144 1.687 -6.833 -1.657 -0.411
beta2_black[14] -1.435 1.738 -6.396 -0.759 -0.065
beta2_black[15] -1.851 2.227 -7.557 -1.402 1.546
beta2_black[16] -1.392 1.739 -4.532 -1.432 1.738
beta3_black[1] 37.874 7.159 19.476 41.427 43.553
beta3_black[2] 30.049 8.054 18.356 29.568 44.647
beta3_black[3] 29.683 7.900 18.456 29.150 45.013
beta3_black[4] 32.009 5.544 19.282 32.581 43.180
beta3_black[5] 30.105 7.907 18.493 29.295 44.756
beta3_black[6] 30.009 7.928 18.505 29.109 45.037
beta3_black[7] 30.154 8.007 18.554 29.260 44.957
beta3_black[8] 30.332 7.927 18.508 29.547 44.919
beta3_black[9] 29.890 7.887 18.402 28.923 44.810
beta3_black[10] 29.791 7.879 18.521 28.579 44.870
beta3_black[11] 29.313 6.852 18.576 28.964 42.880
beta3_black[12] 32.446 1.243 29.533 32.713 33.785
beta3_black[13] 39.273 0.768 37.566 39.350 40.468
beta3_black[14] 37.469 4.837 22.998 38.505 44.978
beta3_black[15] 31.472 7.927 18.790 31.001 45.047
beta3_black[16] 28.201 7.524 18.385 26.502 44.715
beta4_black[1] -0.254 0.184 -0.626 -0.252 0.101
beta4_black[2] 0.248 0.170 -0.083 0.242 0.582
beta4_black[3] -0.936 0.185 -1.304 -0.935 -0.581
beta4_black[4] 0.506 0.225 0.063 0.505 0.935
beta4_black[5] 0.266 2.478 -4.690 0.132 5.172
beta4_black[6] 0.194 2.282 -4.457 0.118 5.294
beta4_black[7] 0.261 2.376 -4.336 0.180 5.704
beta4_black[8] -0.689 0.365 -1.413 -0.679 -0.004
beta4_black[9] 1.473 1.019 -0.090 1.347 3.770
beta4_black[10] 0.026 0.177 -0.320 0.028 0.366
beta4_black[11] -0.693 0.207 -1.108 -0.684 -0.300
beta4_black[12] 0.297 0.333 -0.347 0.293 0.956
beta4_black[13] -1.190 0.210 -1.597 -1.188 -0.788
beta4_black[14] -0.119 0.224 -0.559 -0.122 0.322
beta4_black[15] -0.892 0.205 -1.287 -0.895 -0.492
beta4_black[16] -0.594 0.219 -1.033 -0.592 -0.164
mu_beta0_black[1] 1.223 0.832 -0.630 1.240 2.797
mu_beta0_black[2] 1.554 0.900 -0.556 1.621 3.292
mu_beta0_black[3] 2.202 1.013 -0.025 2.248 4.122
tau_beta0_black[1] 0.782 0.750 0.061 0.557 2.847
tau_beta0_black[2] 2.178 5.387 0.058 0.851 11.903
tau_beta0_black[3] 0.254 0.173 0.049 0.212 0.692
beta0_dsr[11] -3.021 0.273 -3.547 -3.020 -2.491
beta0_dsr[12] 4.477 0.269 3.948 4.475 5.011
beta0_dsr[13] -1.626 0.420 -2.399 -1.587 -1.044
beta0_dsr[14] -4.139 0.473 -5.058 -4.134 -3.217
beta0_dsr[15] -2.406 0.270 -2.929 -2.409 -1.879
beta0_dsr[16] -3.060 0.347 -3.783 -3.062 -2.371
beta1_dsr[11] 4.908 0.287 4.351 4.902 5.457
beta1_dsr[12] 9.381 13.196 2.439 5.489 59.414
beta1_dsr[13] 3.099 0.487 2.503 3.042 4.177
beta1_dsr[14] 6.770 0.505 5.812 6.758 7.784
beta1_dsr[15] 3.598 0.270 3.080 3.602 4.116
beta1_dsr[16] 5.851 0.363 5.152 5.848 6.580
beta2_dsr[11] -8.282 2.335 -13.857 -7.969 -4.724
beta2_dsr[12] -7.104 2.599 -12.682 -6.942 -2.348
beta2_dsr[13] -6.268 2.837 -12.182 -6.226 -0.519
beta2_dsr[14] -6.527 2.478 -12.216 -6.318 -2.484
beta2_dsr[15] -7.591 2.356 -13.098 -7.282 -3.743
beta2_dsr[16] -7.994 2.352 -13.450 -7.628 -4.348
beta3_dsr[11] 43.489 0.150 43.218 43.486 43.775
beta3_dsr[12] 33.964 0.720 32.168 34.110 34.794
beta3_dsr[13] 43.263 0.342 42.871 43.179 43.906
beta3_dsr[14] 43.263 0.141 43.077 43.230 43.628
beta3_dsr[15] 43.469 0.186 43.143 43.460 43.824
beta3_dsr[16] 43.436 0.157 43.171 43.429 43.758
beta4_dsr[11] 0.649 0.212 0.239 0.645 1.073
beta4_dsr[12] 0.324 0.461 -0.583 0.325 1.289
beta4_dsr[13] -0.083 0.208 -0.491 -0.087 0.329
beta4_dsr[14] 0.195 0.253 -0.294 0.192 0.691
beta4_dsr[15] 0.989 0.214 0.567 0.988 1.407
beta4_dsr[16] 0.173 0.225 -0.305 0.175 0.604
beta0_slope[11] -2.006 0.156 -2.316 -2.005 -1.696
beta0_slope[12] -4.686 0.270 -5.226 -4.685 -4.164
beta0_slope[13] -1.438 0.229 -2.000 -1.411 -1.080
beta0_slope[14] -2.646 0.199 -3.036 -2.644 -2.252
beta0_slope[15] -1.703 0.157 -2.001 -1.705 -1.396
beta0_slope[16] -2.762 0.163 -3.079 -2.763 -2.445
beta1_slope[11] 4.381 0.287 3.798 4.381 4.930
beta1_slope[12] 4.796 0.531 3.756 4.779 5.862
beta1_slope[13] 2.713 0.558 2.029 2.614 4.421
beta1_slope[14] 6.008 0.846 4.648 5.910 7.980
beta1_slope[15] 2.032 0.279 1.494 2.027 2.590
beta1_slope[16] 5.289 0.389 4.548 5.281 6.066
beta2_slope[11] 7.814 2.342 4.153 7.502 13.269
beta2_slope[12] 6.397 2.634 2.062 6.199 12.245
beta2_slope[13] 4.461 2.834 0.300 4.102 10.672
beta2_slope[14] 2.739 2.554 0.738 1.533 9.761
beta2_slope[15] 6.517 2.520 2.581 6.219 12.051
beta2_slope[16] 7.273 2.475 3.507 6.888 12.997
beta3_slope[11] 43.498 0.152 43.220 43.497 43.784
beta3_slope[12] 43.449 0.265 43.051 43.423 44.027
beta3_slope[13] 43.570 0.512 42.621 43.611 44.430
beta3_slope[14] 44.668 0.432 43.768 44.721 45.357
beta3_slope[15] 43.596 0.252 43.125 43.609 44.038
beta3_slope[16] 43.471 0.167 43.187 43.457 43.807
beta4_slope[11] -0.451 0.208 -0.858 -0.445 -0.052
beta4_slope[12] -1.152 0.653 -2.631 -1.065 -0.134
beta4_slope[13] 0.173 0.206 -0.226 0.174 0.586
beta4_slope[14] -0.109 0.244 -0.599 -0.108 0.365
beta4_slope[15] -0.198 0.199 -0.592 -0.198 0.196
beta4_slope[16] -0.126 0.224 -0.566 -0.128 0.308
sigma_H[1] 0.195 0.054 0.092 0.193 0.305
sigma_H[2] 0.170 0.030 0.117 0.169 0.237
sigma_H[3] 0.200 0.043 0.125 0.198 0.290
sigma_H[4] 0.419 0.077 0.294 0.411 0.599
sigma_H[5] 0.990 0.216 0.601 0.983 1.448
sigma_H[6] 0.370 0.201 0.030 0.359 0.800
sigma_H[7] 0.299 0.059 0.204 0.291 0.433
sigma_H[8] 0.426 0.099 0.277 0.414 0.633
sigma_H[9] 0.521 0.126 0.327 0.503 0.817
sigma_H[10] 0.217 0.043 0.144 0.213 0.310
sigma_H[11] 0.278 0.046 0.201 0.273 0.382
sigma_H[12] 0.445 0.165 0.212 0.419 0.791
sigma_H[13] 0.214 0.038 0.145 0.212 0.296
sigma_H[14] 0.508 0.097 0.342 0.500 0.719
sigma_H[15] 0.251 0.041 0.184 0.246 0.339
sigma_H[16] 0.225 0.044 0.153 0.219 0.327
lambda_H[1] 2.960 3.710 0.137 1.693 13.273
lambda_H[2] 8.309 7.757 0.753 6.068 28.347
lambda_H[3] 6.136 9.146 0.248 3.186 30.159
lambda_H[4] 0.006 0.004 0.001 0.006 0.018
lambda_H[5] 3.563 7.848 0.034 0.939 24.952
lambda_H[6] 7.538 15.930 0.008 0.582 54.645
lambda_H[7] 0.014 0.010 0.002 0.012 0.041
lambda_H[8] 7.955 10.189 0.012 4.398 37.563
lambda_H[9] 0.015 0.010 0.003 0.013 0.042
lambda_H[10] 0.315 0.767 0.032 0.202 1.074
lambda_H[11] 0.252 0.362 0.012 0.132 1.130
lambda_H[12] 4.815 6.223 0.210 2.825 21.074
lambda_H[13] 3.221 2.783 0.253 2.403 10.513
lambda_H[14] 3.626 4.357 0.229 2.297 15.020
lambda_H[15] 0.037 0.429 0.004 0.017 0.124
lambda_H[16] 1.247 1.742 0.059 0.661 5.864
mu_lambda_H[1] 4.349 1.930 1.143 4.178 8.540
mu_lambda_H[2] 3.779 1.956 0.555 3.623 7.871
mu_lambda_H[3] 3.481 1.816 0.802 3.241 7.684
sigma_lambda_H[1] 8.597 4.329 1.951 7.948 18.393
sigma_lambda_H[2] 8.182 4.646 0.948 7.591 18.271
sigma_lambda_H[3] 6.117 3.885 0.965 5.333 16.082
beta_H[1,1] 6.869 1.095 4.328 7.013 8.603
beta_H[2,1] 9.863 0.495 8.752 9.888 10.785
beta_H[3,1] 8.004 0.779 6.199 8.092 9.278
beta_H[4,1] 9.293 7.751 -6.833 9.558 23.897
beta_H[5,1] 0.112 2.267 -4.789 0.278 4.167
beta_H[6,1] 3.097 4.052 -7.247 4.525 7.739
beta_H[7,1] 1.105 5.621 -11.429 1.569 10.872
beta_H[8,1] 1.882 6.235 -2.557 1.262 7.954
beta_H[9,1] 13.196 5.858 1.360 13.005 25.257
beta_H[10,1] 7.090 1.701 3.616 7.162 10.390
beta_H[11,1] 5.214 3.419 -2.624 5.941 9.911
beta_H[12,1] 2.620 1.031 0.842 2.541 4.869
beta_H[13,1] 9.043 0.911 7.122 9.102 10.557
beta_H[14,1] 2.196 0.995 0.236 2.199 4.176
beta_H[15,1] -5.796 4.054 -13.252 -6.040 3.172
beta_H[16,1] 3.175 2.353 -0.883 2.963 8.578
beta_H[1,2] 7.902 0.251 7.391 7.909 8.378
beta_H[2,2] 10.023 0.137 9.756 10.021 10.292
beta_H[3,2] 8.950 0.198 8.561 8.951 9.339
beta_H[4,2] 3.570 1.474 0.768 3.490 6.605
beta_H[5,2] 1.964 0.947 0.064 1.967 3.799
beta_H[6,2] 5.723 1.091 3.168 5.903 7.410
beta_H[7,2] 2.472 1.084 0.575 2.426 4.815
beta_H[8,2] 2.842 1.578 -0.090 3.116 4.241
beta_H[9,2] 3.430 1.111 1.236 3.428 5.692
beta_H[10,2] 8.178 0.344 7.443 8.190 8.832
beta_H[11,2] 9.724 0.614 8.825 9.608 11.104
beta_H[12,2] 3.935 0.367 3.238 3.927 4.673
beta_H[13,2] 9.114 0.249 8.656 9.110 9.599
beta_H[14,2] 4.003 0.348 3.330 4.004 4.704
beta_H[15,2] 11.311 0.719 9.795 11.339 12.616
beta_H[16,2] 4.587 0.808 3.040 4.586 6.138
beta_H[1,3] 8.494 0.243 8.053 8.484 8.995
beta_H[2,3] 10.078 0.117 9.849 10.076 10.313
beta_H[3,3] 9.620 0.164 9.298 9.619 9.949
beta_H[4,3] -2.474 0.884 -4.275 -2.441 -0.799
beta_H[5,3] 3.865 0.614 2.627 3.867 5.032
beta_H[6,3] 8.186 1.225 6.487 7.823 10.810
beta_H[7,3] -2.547 0.734 -3.966 -2.540 -1.141
beta_H[8,3] 5.316 0.715 4.617 5.187 7.157
beta_H[9,3] -2.736 0.733 -4.257 -2.721 -1.320
beta_H[10,3] 8.736 0.273 8.222 8.731 9.294
beta_H[11,3] 8.536 0.282 7.923 8.563 9.020
beta_H[12,3] 5.242 0.321 4.462 5.281 5.772
beta_H[13,3] 8.849 0.175 8.493 8.853 9.186
beta_H[14,3] 5.678 0.271 5.101 5.697 6.191
beta_H[15,3] 10.388 0.325 9.777 10.385 11.038
beta_H[16,3] 6.417 0.611 5.073 6.483 7.402
beta_H[1,4] 8.277 0.171 7.911 8.287 8.577
beta_H[2,4] 10.130 0.122 9.873 10.137 10.351
beta_H[3,4] 10.120 0.168 9.745 10.137 10.404
beta_H[4,4] 11.784 0.451 10.882 11.789 12.659
beta_H[5,4] 5.521 0.766 4.309 5.437 7.348
beta_H[6,4] 7.110 0.899 5.057 7.360 8.331
beta_H[7,4] 8.213 0.348 7.508 8.215 8.871
beta_H[8,4] 6.675 0.318 5.895 6.701 7.146
beta_H[9,4] 7.199 0.468 6.279 7.196 8.137
beta_H[10,4] 7.756 0.240 7.314 7.746 8.245
beta_H[11,4] 9.297 0.204 8.893 9.294 9.704
beta_H[12,4] 7.128 0.215 6.722 7.121 7.563
beta_H[13,4] 9.011 0.146 8.707 9.016 9.288
beta_H[14,4] 7.653 0.216 7.227 7.657 8.090
beta_H[15,4] 9.456 0.237 8.988 9.453 9.911
beta_H[16,4] 9.215 0.221 8.824 9.195 9.691
beta_H[1,5] 8.977 0.149 8.675 8.981 9.254
beta_H[2,5] 10.778 0.095 10.593 10.775 10.979
beta_H[3,5] 10.920 0.172 10.615 10.912 11.270
beta_H[4,5] 8.391 0.467 7.507 8.379 9.323
beta_H[5,5] 5.375 0.596 3.989 5.432 6.381
beta_H[6,5] 8.766 0.606 7.870 8.635 10.207
beta_H[7,5] 6.795 0.337 6.138 6.795 7.456
beta_H[8,5] 8.232 0.259 7.859 8.206 8.823
beta_H[9,5] 8.200 0.463 7.290 8.195 9.135
beta_H[10,5] 10.077 0.234 9.608 10.082 10.527
beta_H[11,5] 11.535 0.233 11.079 11.533 11.999
beta_H[12,5] 8.477 0.201 8.060 8.477 8.887
beta_H[13,5] 10.011 0.130 9.758 10.011 10.264
beta_H[14,5] 9.179 0.237 8.747 9.168 9.682
beta_H[15,5] 11.162 0.242 10.670 11.163 11.632
beta_H[16,5] 9.957 0.166 9.613 9.961 10.270
beta_H[1,6] 10.189 0.197 9.850 10.176 10.626
beta_H[2,6] 11.515 0.110 11.295 11.514 11.729
beta_H[3,6] 10.814 0.159 10.463 10.826 11.100
beta_H[4,6] 12.909 0.820 11.278 12.941 14.527
beta_H[5,6] 5.893 0.599 4.783 5.870 7.141
beta_H[6,6] 8.778 0.630 7.073 8.876 9.719
beta_H[7,6] 9.828 0.558 8.756 9.831 10.945
beta_H[8,6] 9.494 0.346 8.797 9.532 9.972
beta_H[9,6] 8.479 0.772 6.974 8.470 10.007
beta_H[10,6] 9.516 0.320 8.806 9.543 10.082
beta_H[11,6] 10.805 0.366 10.015 10.832 11.457
beta_H[12,6] 9.373 0.253 8.887 9.363 9.908
beta_H[13,6] 11.063 0.161 10.775 11.059 11.408
beta_H[14,6] 9.865 0.287 9.289 9.868 10.409
beta_H[15,6] 10.875 0.427 10.039 10.876 11.703
beta_H[16,6] 10.552 0.225 10.063 10.570 10.958
beta_H[1,7] 10.845 0.911 8.609 10.961 12.306
beta_H[2,7] 12.211 0.436 11.246 12.218 13.035
beta_H[3,7] 10.544 0.675 9.044 10.618 11.642
beta_H[4,7] 2.329 4.145 -5.941 2.293 10.640
beta_H[5,7] 6.474 1.869 3.119 6.371 11.038
beta_H[6,7] 9.474 2.384 4.740 9.452 15.399
beta_H[7,7] 10.676 2.843 5.175 10.708 16.302
beta_H[8,7] 11.043 1.308 9.256 10.921 13.689
beta_H[9,7] 4.375 3.965 -3.845 4.442 11.979
beta_H[10,7] 9.783 1.448 7.163 9.676 13.026
beta_H[11,7] 10.998 1.808 7.692 10.880 14.925
beta_H[12,7] 10.026 0.922 8.017 10.087 11.603
beta_H[13,7] 11.662 0.764 9.733 11.771 12.849
beta_H[14,7] 10.484 0.955 8.442 10.556 12.108
beta_H[15,7] 12.110 2.207 7.758 12.090 16.545
beta_H[16,7] 12.148 1.182 10.349 11.948 14.991
beta0_H[1] 8.596 13.461 -20.662 8.728 36.111
beta0_H[2] 10.582 6.549 -2.305 10.703 23.693
beta0_H[3] 9.993 9.953 -9.025 9.898 29.867
beta0_H[4] 2.166 176.800 -348.738 7.181 346.028
beta0_H[5] 4.036 24.403 -40.155 4.350 49.517
beta0_H[6] 7.762 49.712 -100.113 7.567 122.201
beta0_H[7] 1.445 128.782 -257.912 3.544 252.725
beta0_H[8] 6.156 53.216 -25.234 6.582 36.350
beta0_H[9] 7.642 122.218 -228.711 6.116 266.085
beta0_H[10] 8.911 33.055 -60.521 9.632 74.817
beta0_H[11] 8.939 48.803 -90.956 10.069 108.200
beta0_H[12] 6.562 11.073 -14.359 6.908 28.604
beta0_H[13] 9.624 11.092 -10.527 9.613 29.787
beta0_H[14] 7.040 11.254 -15.192 7.206 29.438
beta0_H[15] 9.713 103.427 -205.679 10.613 219.768
beta0_H[16] 7.861 21.507 -36.473 7.923 51.153